A090407 a(n) = Sum_{k = 0..n} C(4*n + 1, 4*k).

1, 6, 136, 2016, 32896, 523776, 8390656, 134209536, 2147516416, 34359607296, 549756338176, 8796090925056, 140737496743936, 2251799780130816, 36028797153181696, 576460751766552576, 9223372039002259456

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..800

Index entries for linear recurrences with constant coefficients, signature (12,64).

Formula

From Harvey P. Dale, Jan 19 2012: (Start)

a(0) = 1, a(1) = 6, a(n) = 12*a(n-1)+64*a(n-2).

G.f.: (6*x-1)/(64*x^2+12*x-1). (End)

a(n) = (1/2) * 4^n * (4^n + (-1)^n). - Peter Bala, Feb 06 2019

Mathematica

Table[Sum[Binomial[4n+1, 4k], {k, 0, n}], {n, 0, 30}] (* or *) LinearRecurrence[ {12, 64}, {1, 6}, 30] (* Harvey P. Dale, Jan 19 2012 *)

Crossrefs

Cf. A070775, A001025, A090408, A038503.

Sequence in context: A196703 A196852 A196946 * A222915 A367531 A245104

Adjacent sequences: A090404 A090405 A090406 * A090408 A090409 A090410

Keyword

easy,nonn

Author

Paul Barry, Nov 29 2003

Status

approved